Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 108 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹280 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹280 (b) ₹140 (c) ₹28 (d) ₹252
2. 2.If 8 mangoes cost ₹64, how much do 11 mangoes cost? (a) ₹88 (b) ₹67 (c) ₹704 (d) ₹96
3. 3.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹45 (b) ₹90 (c) ₹10 (d) ₹80
4. 4.If 4 pens cost ₹68, how much do 12 pens cost? (a) ₹204 (b) ₹816 (c) ₹221 (d) ₹76
5. 5.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹144 (b) ₹48 (c) ₹192 (d) ₹240
6. 6.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹117 (b) ₹29 (c) ₹145 (d) ₹116
7. 7.If 5 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹120 (b) ₹29 (c) ₹30 (d) ₹24
8. 8.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 6 days (d) 12 days
9. 9.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹98 (b) ₹77 (c) ₹56 (d) ₹14
10. 10.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 24 days (d) 25 days
11. 11.If 5 mangoes cost ₹55, how much do 12 mangoes cost? (a) ₹132 (b) ₹660 (c) ₹62 (d) ₹143
12. 12.If 8 pens cost ₹144, how much do 9 pens cost? (a) ₹145 (b) ₹162 (c) ₹1296 (d) ₹180
13. 13.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 12 days (d) 8 days
14. 14.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 8 days (d) 2 days
15. 15.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹344 (b) ₹215 (c) ₹387 (d) ₹43
16. 16.If 5 pens cost ₹40, how much do 6 pens cost? (a) ₹240 (b) ₹41 (c) ₹48 (d) ₹56
17. 17.If 5 mangoes cost ₹35, how much do 7 mangoes cost? (a) ₹245 (b) ₹49 (c) ₹56 (d) ₹37
18. 18.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 5 days (d) 4 days
19. 19.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 8 days (d) 17 days
20. 20.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹49 (b) ₹7 (c) ₹63 (d) ₹35
21. 21.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 7 days (d) 18 days
22. 22.If 8 kites cost ₹112, how much do 9 kites cost? (a) ₹126 (b) ₹1008 (c) ₹113 (d) ₹140
23. 23.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
24. 24.If 2 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹396 (b) ₹45 (c) ₹216 (d) ₹198
25. 25.If 4 pens cost ₹12, how much do 10 pens cost? (a) ₹33 (b) ₹18 (c) ₹30 (d) ₹120
26. 26.If 5 pens cost ₹60, how much do 11 pens cost? (a) ₹144 (b) ₹132 (c) ₹66 (d) ₹660
27. 27.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
28. 28.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 16 days (d) 4 days
29. 29.₹143 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹99 (d) ₹88
30. 30.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹92 (d) ₹161
31. 31.If 7 mangoes cost ₹126, how much do 8 mangoes cost? (a) ₹127 (b) ₹162 (c) ₹1008 (d) ₹144
32. 32.If 4 pens cost ₹84, how much do 5 pens cost? (a) ₹85 (b) ₹420 (c) ₹126 (d) ₹105
33. 33.If 2 kites cost ₹46, how much do 9 kites cost? (a) ₹53 (b) ₹230 (c) ₹414 (d) ₹207
34. 34.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 5 days (d) 4 days
35. 35.If 4 mangoes cost ₹28, how much do 8 mangoes cost? (a) ₹63 (b) ₹32 (c) ₹56 (d) ₹224
36. 36.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 13 days (d) 9 days
37. 37.If 5 kites cost ₹40, how much do 6 kites cost? (a) ₹48 (b) ₹56 (c) ₹240 (d) ₹41
38. 38.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 14 days (d) 15 days
39. 39.₹517 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹141 (b) ₹423 (c) ₹47 (d) ₹376
40. 40.If 5 notebooks cost ₹85, how much do 12 notebooks cost? (a) ₹1020 (b) ₹221 (c) ₹92 (d) ₹204

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